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Proof step 177 from proof fsync-inode-inv (previous step)

files[m] = mkfile(m0, md0, # links(m, dirs), content), err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ icache, m ∈ files, ¬ icache[m].dirty ⊦ ⟪icache_set_status#(m, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = files[m].nlink)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 178:
files[m] = mkfile(m0, md0, # links(m, dirs), content), icache[m] = mkientry(boolvar, inode), ¬ boolvar, err = ESUCCESS, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ files, m ∈ icache ⊦ ⟪icache_set_status#(m, false; err, icache)⟫ (icache-cons(icache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ # links(m, dirs) = files[m].nlink)

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[m], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode